Performance Analysis of Correlation Measures for Nominal Data

Abstract

Given the widespread presence of dichotomous data in social sciences, use of correct correlation technique is required to determine relationship between variables. The research, therefore, provide selection of correlation measure when analyzing nominal data, that include Pearson, phi, tetrachoric, point biserial, biserial and correlation coefficient V. The objective of research is to identify best measure of association for nominal data, in terms of size, power and bias in an estimate of statistic, by varying sample size, population correlation, level of significance and underlying distributions of continuous variable. The results from the simulation studies show that power of the correlation technique increased with an increase in sample size and population correlation. Even though, Pearson provides better control over power and size of test for nominal data, it gives estimates that are moderately biased. On the other hand, correlation technique developed for respective categorization of nominal data gives unbiased estimates and are, therefore, recommended.